Speedy Sidney

Two trains set off at the same time from each end of a single straight railway line. A very fast bee starts off in front of the first train and flies continuously back and forth between the two trains. How far does Sidney fly before he is squashed between the two trains?
Age
11 to 14
Challenge level
filled star filled star filled star
Exploring and noticing Working systematically Conjecturing and generalising Visualising and representing Reasoning, convincing and proving
Being curious Being resourceful Being resilient Being collaborative

Problem



Two trains set off at the same time from each end of a single straight railway line which is 100 km long.

The first train travels at a constant speed of 55 km/h. The second train travels at a constant speed of 70 km/h.

A very fast bee, Sidney travels at 100 km/h. Sidney starts off in front of the first train and flies continuously back and forth between the two trains.

How far does Sidney fly before he is squashed between the two trains?



Extension:

How could you alter the problem so that Sidney flies exactly 100 km?

(Apologies to bee lovers everywhere!)